Trying to extrude bottom wall layout to build a house?
Alright, first things first. Let's identify your problems, which I did after a couple minutes.

Problems


You can Remove Doubles to remove 4,332 vertices.
Your bottom area has a tiny amount of thickness, which is preventing Extrude from working correctly.
Normals are all over the place.
Some faces are missing.


Solution

Beginning from your uploaded .blend file.


Begin by keying A twice to select everything and key W > Remove Doubles.
Enter Front Orthographic View by keying Numpad 1 and Numpad 5. This will allow us to remove the top and few walls that extruded correctly.
Key Ctrl + Tab, 3 to enter Face Mesh Select Mode and Z to enter Wireframe View. Key A to deselect everything. Face select mode allows us to select the correctly extruded middle faces. Wireframe allows us to select vertices that are obscured by other parts of the mesh, rather than just the faces we can see.
Use Box Select to select these faces:
 
Key X and select Faces to delete these faces. If you zoom in very close on the bottom, you can see its thickness:
 
Key Z to exit Wireframe View and return to Solid View. Key Numpad 7 to enter Top View.
Box Select the entire grid. Because you are in Orthographic Solid View, only the top faces will be selected.
Key X and select Vertices to delete all top vertices. This will remove the mesh interference.
However, if you try to extrude now, you may get weird glitches. You must select everything with A and use Ctrl + N to Recalculate Normals.
You may want to Fill in some faces now.
 
You can now use E to Extrude up on the Z-Axis.
Select everything with A one last time and use Ctrl + N once again to finish touching up Normals.


Finished Product: